The oversampling phasing method

Abstract

Sampling the diffraction pattern of a finite specimen more finely than the Nyquist frequency (the inverse of the size of the diffracting specimen) corresponds to surrounding the electron density of the specimen with a no-density region. When the no-density region is bigger than the electron-density region, sufficient information is recorded so that the phase information can be retrieved from the oversampled diffraction pattern, at least in principle. By employing an iterative algorithm, the phase information from the oversampled diffraction pattern of a micrometre-sized test specimen has been successfully retrieved. This method is believed to be able to open a door for high-resolution three-dimensional structure determination of complex and non-crystalline biological specimens, i.e. whole cells and sub-micrometre molecular clusters and micrometre-sized protein crystals. With the possible appearance in the future of X-ray free-electron lasers, it may become possible to image single molecules by recording diffraction patterns before radiation damage manifests itself.